Author Archives: Justin Allen

The solution I have chosen is as follows. Use bezier curve that has 2 control points, these are each end of the line. Then set the rotation based on the tangent at the midpoint. Code shown below.

private static Vector3 CalculateTangent(float t, Vector3 p0, Vector3 p1)
{
    float a = 1 - t;
    float b = a * 6 * t;
    a = a * a * 3;
    float c = t * t * 3;
    return (-a * p0) + (c * p1);
}

public Mesh CalculateMesh()
{
    Mesh mesh = new Mesh();
    List<Vector3> verts = new List<Vector3>();
    Quaternion quaternion = Quaternion.LookRotation(CalculateTangent(0.5f, startPosition, endPosition));
    verts.Add( (quaternion * new Vector3(-widthOffset, 0.0f, 0.0f)) + startPosition );   // 0
    verts.Add( (quaternion * new Vector3(widthOffset, 0.0f, 0.0f)) + startPosition );    // 1
    verts.Add( (quaternion * new Vector3(-widthOffset, height, 0.0f)) + startPosition ); // 2
    verts.Add( (quaternion * new Vector3(widthOffset, height, 0.0f)) + startPosition );  // 3
    verts.Add( (quaternion * new Vector3(-widthOffset, 0.0f, 0.0f)) + endPosition );     // 4
    verts.Add( (quaternion * new Vector3(widthOffset, 0.0f, 0.0f)) + endPosition );      // 5
    verts.Add( (quaternion * new Vector3(-widthOffset, height, 0.0f)) + endPosition );   // 6
    verts.Add( (quaternion * new Vector3(widthOffset, height, 0.0f)) + endPosition );    // 7
    Face[] faces = new Face[] {
        new Face(0, 1, 2, 3),
        new Face(0, 1, 4, 5),
        new Face(0, 2, 4, 6),
        new Face(1, 3, 5, 7),
        new Face(2, 3, 6, 7),
        new Face(4, 5, 6, 7)
    };
    List<int> tris = new List<int>();
    for (int i = 0; i < faces.Length; i++)
    {
        tris.AddRange(faces[i].Tris());
    }
    mesh.vertices = verts.ToArray();
    mesh.triangles = tris.ToArray();
    return mesh;
}

This is a problem I have encountered while working on my personal side project, a simulation game. Unity mesh allows developers to dynamically create meshes at runtime. Meshes take an array of Vector3s and an array of Integers to create the mesh. Vector3 is a data type that stores the X, Y, and Z positions as floating point numbers.

Creating an array of Vector3s, which is the vertices, and the array of integers; signifying the triangles; allows the developer to make any shape they would like. The array of integers which is grouped into threes, tells the mesh system which three vertices, by index from the array of vertices, make up the triangle. All triangles are rendered as one sided triangles, developers can change which side is rendered by swapping the first and last indexes of the triangle. Example 1,2,3 should be come 3,2,1 to reverse it.

Wall generation will utilize a starting and ending point, passed in as Vector3s. They also have an extrude height and an extrude width. This will allow a lot of customization in the long run. Below is an image showing the wall generation tool with two selected points that are 3 units apart in the X direction.

However when you make the same distance wall in the Z direction it looks more like the image below.

The problem is when the walls are generated in the Z direction their extrude outward from the input points isn’t calculated correctly and makes the wall flat. Below is the code used to add the vertices to the list of vertices.

verts.Add(startPosition + new Vector3(0.0f, 0.0f, -widthOffset)); // 0
verts.Add(startPosition + new Vector3(0.0f, 0.0f, widthOffset));  // 1
verts.Add(startPosition + new Vector3(0.0f, height, -widthOffset)); // 2
verts.Add(startPosition + new Vector3(0.0f, height, widthOffset));  // 3
verts.Add(endPosition + new Vector3(0.0f, 0.0f, -widthOffset)); // 4
verts.Add(endPosition + new Vector3(0.0f, 0.0f, widthOffset));  // 5
verts.Add(endPosition + new Vector3(0.0f, height, -widthOffset));// 6
verts.Add(endPosition + new Vector3(0.0f, height, widthOffset)); // 7

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Potential Solutions

Solution #1: Create the object using the distance between the start position and end position in the X(or Z) direction and then rotate the object towards the end point. This might work if you use the origin as the start position and then set transform.position on the object to move it to the correct position.

Solution #2: Use mathematic formula derived from the formula to calculate the tangent of a bezier curve to calculate the rotation needed at the start and end points.

Solution #3: Use bezier curve that has 4 points and set the two control points to the midpoint of the line. I have already implemented a 4 point bezier wall generation system, wouldn’t be too hard to convert. Four point bezier curve is shown below in wireframe mode.

Dynamic generation of polygonal 2d meshes is a useful stepping stone to more dynamic shapes. Unity Mesh object can be broken down into two major components, an array of Vector3s and an array of integers. The simplest polygons have equal angles and side lengths, this is an easy calculation to do; to calculate the X and Y values we use Cosine and Sine functions.

float angle = Mathf.Deg2Rad * ( 360 / sides );
Vector3[] verts = new Vector3[sides];
for (int i = 0; i < verts.Length; i++)
{
    float h = angle * i;
    float x = Mathf.Cos(h) * distance;
    float y = Mathf.Sin(h) * distance;
    verts[i] = new Vector3(x, y, 0.0f);
 }

The next step of making a mesh dynamically is to determine the triangles that the face is made up of. We first figure out how many triangles we require, this can be done by taking the number of vertices and subtract 2. Now we can walk thru each triangle and determine the index of each vertex. Making the simple assumption that every triangle of the face is going to start at the first vertex; we then have to determine the two other vertices. Once we determine the vertex indices of the individual triangles we then have to add them to the mesh triangles indices list. Before we can add them to that array we must order them so that the faces are facing the correct direction.

List<int> triangles = new List<int>();
int triangleCount = verts.Length - 2;
for (int i = 0; i < triangleCount; i++)
{
    int a = 0;
    int b = 1 + i;
    int c = 2 + i;
    switch (faceDirection)
    {
        case FaceDirection.FRONT:
            triangles.AddRange(new int[] { c, b, a });
            break;
        case FaceDirection.BACK:
            triangles.AddRange(new int[] { a, b, c });
            break;
        case FaceDirection.BOTH:
            triangles.AddRange(new int[] { c, b, a });
            triangles.AddRange(new int[] { a, b, c });
            break;
    }
}

Now that we have both the components we need, time to apply them to the mesh object.

Mesh mesh = new Mesh();
mesh.vertices = verts;
mesh.triangles = triangles.ToArray();

Once you have the mesh object, you will have to set it to the MeshFilter component on a game object. This can be used in both the Start and Update methods.